It solves the many problems that arise from the invalid (general) Riemann Hypothesis.
Any set becomes measurable. Measure theory can do without σ-algebras and zero sets. It is simpler overall.
It solves linear inequalities and calculates eigenvalues and vectors in quadratic time.
All (finite) non-deterministic problems can be solved deterministically.
The topology becomes simpler: both represent redundant terms.
They continuously fill the abrupt gap from finite to infinite numbers.
It allows limiting to (infinitely) rational numbers and simplifying the theory.
They are the basis for counting the elements of all existing sets.
They make it possible to work with irregular distances in analysis and they greatly simplify it.
It is simpler, more precise and more general than the previous integral definitions.
© 2020 by Boris Haase